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- Title
M-fuzzifying normed vector spaces.
- Authors
Wang, Yongchao; Shi, Fu-Gui
- Abstract
In this paper, we introduce the concept of M-fuzzifying norm, which can be seen as a fuzzy co-norm. Fuzzy norm plays a key role in fuzzy functional analysis, which can be applied in theoretical computer science and information theory. We also present a characterization of M-fuzzifying norm using cut-sets. Furthermore, we prove that Morsi's fuzzy norm and M-fuzzifying norm are equivalent when M = [ 0 , 1 ] . In addition, we show that an M-fuzzifying norm can induce an M-fuzzifying topology. Finally, we study an M-fuzzifying Banach space. We also study the boundedness of M-fuzzifying normed space. In particular, the mapping corresponding to the degree of fuzzifying boundedness is exactly an M-fuzzifying bornology.
- Subjects
VECTOR spaces; BANACH spaces; INFORMATION theory; COMPUTER science; TOPOLOGY; FUNCTIONAL analysis
- Publication
Computational & Applied Mathematics, 2024, Vol 43, Issue 4, p1
- ISSN
0101-8205
- Publication type
Article
- DOI
10.1007/s40314-024-02697-4